This is a SWOG study designed to compare complete response rate, overall survival and progression free survival of subject in aggressive NHL. It compares conventional chemotherapy, (CHOP X 8) plus (possible autologous BMT) following progression to a short course of induction chemotherapy (CHOP X 4) followed by early transplantation. There has been little progress in the conventional management of newly diagnosed patients with diffuse aggressive NHL. A logical result would be to investigate early high dose transplant therapy for patients with high risk disease to improve the curability of this tumor. If as suggested by the lower CR rates for these patients, drug resistance appears early in these high risk patients, a potentially useful strategy would be to perform the transplant early to prevent the development of a large tumor burden that is drug resistant. While early transplant of high risk patients may improve progression-free survival, overall survival is the more important endpoint given the value of transplantation for relapsing disease.